Quadratic optimum trading positions for asian options

Abstract

A trading position evaluation system for evaluating trading positions that are globally optimum in market measure includes a trading parameters determination module to determine at a trading time instance from amongst a plurality of trading time instances obtained from a trader, a plurality of trading parameters pertaining to a path-dependent Asian option based on ECC data and market data, retrieved from a database. The trading parameters are indicative of information relating to the path-dependent Asian option. Based on the trading parameters, a position evaluation module evaluates a trading position in the underlying asset at the trading time instance based on the plurality of trading parameters to minimize global variance of profit and loss to the trader.

I/we claim: 
     
         1 . A trading position evaluation system comprising:
 a processor;   a parameter determination module, coupled to the processor, to
 determine, at a trading time instance from amongst a plurality of trading time instances obtained from a trader, a plurality of trading parameters and pricing option parameters pertaining to a path-dependent Asian option based on ECC data and market data, retrieved from a database, wherein the plurality of trading parameters is indicative of information relating to the path-dependent Asian option, and 
 wherein the ECC data comprises data associated with the path-dependent Asian option and an underlying asset of the path-dependent Asian option, and the market data comprises annualized rate of return of the underlying asset, annualized volatility of the underlying asset, and risk-free interest rate of market; 
 compute geometric average of the pricing option parameters, wherein the geometric average is computed at pre-set time instances between the time of initiation and the time of maturity of the Asian option; and 
   a position evaluation module, coupled to the processor, to evaluate a trading position in the underlying asset at the trading time instance based on the plurality of trading parameters and the geometric average of the pricing option parameters, wherein the trading position minimizes global variance of profit and loss to the trader.   
     
     
         2 . The trading position evaluation system as claimed in  claim 1 , wherein the plurality of trading parameters comprises mean return of the arithmetic-returns of the underlying asset of the ECC, root mean square of the arithmetic-returns of the underlying asset price process, an accumulated trading gain until a current trading time instance, a term representing the normalized cross-moment between discounted payoff of the ECC and the arithmetic return of the underlying asset of the ECC, a quadratic approximation of the option price at the time of initiation of the ECC, a scaled option price, and a shifted scaled option price at a trading instance. 
     
     
         3 . The trading position evaluation system as claimed in  claim 2 , wherein the parameter determination module is coupled to the processor to determine the mean return of arithmetic-returns of the underlying asset of the ECC based on the risk-free interest rate, the annualized rate of return of the underlying asset, and time difference between two consecutive trading time instances. 
     
     
         4 . The trading position evaluation system as claimed in  claim 2 , wherein the parameter determination module is coupled to the processor to determine the root mean square of the underlying asset based on the risk-free interest rate, the annualized rate of return of the underlying asset, the annualized volatility of the underlying asset, and time difference between two consecutive trading time instances. 
     
     
         5 . The trading position evaluation system as claimed in  claim 2 , wherein the parameter determination module is coupled to the processor to determine the quadratic approximation price of the ECC based the risk-free interest rate, the annualized rate of return of the underlying asset, the annualized volatility of the underlying asset, price of the ECC at the time of initiation, the mean return of the arithmetic-returns of the underlying asset, and the spot price of the underlying asset. 
     
     
         6 . The trading position evaluation system as claimed in  claim 1 , wherein the pricing option parameters include a scaled option price and a shifted scaled option price. 
     
     
         7 . The trading position evaluation system as claimed in  claim 1  further comprising a market parameter computation module, coupled to the processor, to:
 retrieve historical data of the underlying asset from the database, wherein the historical data comprises historical market prices of the underlying asset; 
 compute log-returns of the underlying asset based on the historical data; 
 generate a plurality of scenarios based on fitting the log-returns into a best-fit distribution; 
 fit the plurality of scenarios to a Normal distribution to compute rate of return of the underlying asset and volatility of the underlying asset; and 
 annualize the rate of return and the volatility to obtain the annualized rate of return and an annualized volatility. 
 
     
     
         8 . The trading position evaluation system as claimed in  claim 1 , wherein the ECC data comprises time of initiation of the path-dependent Asian option, time to maturity of the path-dependent Asian option, premium, spot price of the underlying asset, strike price of the path-dependent Asian option, and current market price of call and put options written on the underlying asset of the path-dependent Asian option. 
     
     
         9 . The trading position evaluation system as claimed in  claim 1  further comprising an interest rate calculation module, coupled to the processor, to calculate the risk-free interest rate of the market based on the ECC data. 
     
     
         10 . The trading position evaluation system as claimed in  claim 7 , wherein the best-fit distribution is one of a Normal distribution, a Poisson distribution, and a T-distribution. 
     
     
         11 . A computer-implemented method for evaluating trading positions for a path-dependent Asian option that are quadratic optimum in a market measure, wherein the method comprises:
 receiving, by a processor, a plurality of trading time instances from a trader;   retrieving, by the processor, ECC data and market data associated with the path-dependent Asian option from a database, wherein the ECC data comprises data associated with the path-dependent Asian option and an underlying asset of the path-dependent Asian option, and the market data comprises annualized rate of return and annualized volatility of the underlying asset, and risk-free interest rate of market;   determining, by the processor, a plurality of trading parameters and the pricing option parameters pertaining to the path-dependent Asian option at each of a plurality of trading time instances, based on the ECC data and the market data, wherein the plurality of trading parameters is indicative of information relating to the path-dependent Asian option;   computing, by the processor, a geometric average of the pricing option parameters at pre-set time instances between the time of initiation and the time of maturity of the Asian option; and   evaluating, by the processor, a trading position in the underlying asset at each of the plurality of trading time instances based on the plurality of trading time instances, wherein the trading position minimizes global variance of profit and loss to the trader.   
     
     
         12 . The method as claimed in  claim 11  further comprising:
 retrieving, by the processor, historical data for a predefined period from the database; 
 evaluating, by the processor, log-returns of the underlying asset based on the historical data; 
 generating, by the processor, a plurality of scenarios based on fitting the log-returns into a best-fit distribution; 
 fitting, by the processor, the plurality of scenarios to a normal distribution to compute the rate of return of the underlying asset and the volatility of the underlying asset; and 
 annualizing, by the processor, the rate of return and the volatility to obtain the annualized rate of return and the annualized volatility. 
 
     
     
         13 . The method as claimed in  claim 12 , wherein the historical data comprises historical market prices of the underlying asset obtained from a data source. 
     
     
         14 . The method as claimed in  claim 11 , wherein the ECC data comprises time of initiation of the path-dependent Asian option, time to maturity of the path-dependent Asian option, premium, spot price of the underlying asset, strike price of the path-dependent Asian option, and current market price of call and put options written on the underlying asset of the path-dependent Asian option. 
     
     
         15 . The method as claimed in  claim 11  further comprising calculating, by the processor, the risk-free interest rate of the market based on the ECC data. 
     
     
         16 . A non-transitory computer-readable medium having embodied thereon a computer program for executing a method for evaluating trading positions for a path-dependent Asian option that are quadratic optimum in a market measure, wherein the method comprises:
 receiving a plurality of trading time instances from a trader;   retrieving ECC data and market data associated with the path-dependent Asian option from a database, wherein the ECC data comprises data associated with the path-dependent Asian option and an underlying asset of the path-dependent Asian option, and the market data comprises annualized rate of return and annualized volatility of the underlying asset, and risk-free interest rate of market;   determining a plurality of trading parameters pertaining to the path-dependent Asian option at each of a plurality of trading time instances, based on the ECC data and the market data, wherein the plurality of trading parameters is indicative of information relating to the path-dependent Asian option; and   evaluating a trading position in the underlying asset at each of the plurality of trading time instances based on the plurality of trading time instances, wherein the trading position minimizes global variance of profit and loss to the trader.   
     
     
         17 . The non-transitory computer-readable medium as claimed in  claim 16 , wherein the method further comprises:
 retrieving historical data for a predefined period from the database;   evaluating log-returns of the underlying asset based on the historical data;   generating a plurality of scenarios based on fitting the log-returns into a best-fit distribution;   fitting the plurality of scenarios to a normal distribution to compute the volatility and the rate of return of the underlying asset; and   annualizing the volatility and the rate of return to obtain the annualized volatility and the annualized rate of return.   
     
     
         18 . The non-transitory computer-readable medium as claimed in  claim 17 , wherein the historical data comprises historical market prices of the underlying asset obtained from a data source. 
     
     
         19 . The non-transitory computer-readable medium as claimed in  claim 16 , wherein the method further comprises calculating the risk-free interest rate of the market based on the ECC data.